As mentioned in the text, the tangent line to a smooth curve r(t) = (t)i + g(t)j + h(t)k at t = t 0 is

As mentioned in the text, the tangent line to a smooth curve r(t) = ƒ(t)i + g(t)j + h(t)k at t = t₀ is the line that passes through the point (ƒ(t₀), g(t₀), h(t₀)) parallel to v(t₀), the curve’s velocity vector at t₀. Find parametric equations for the line that is tangent to the given curve at the given parameter value t = t₀.

r(t) = t² i + (2t - 1)j + t³k, t₀ = 2